Batch Reactors for Hydrogen Production: Theoretical Analysis and

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Ind. Eng. Chem. Res. 2009, 48, 5610–5623

Batch Reactors for Hydrogen Production: Theoretical Analysis and Experimental Characterization David L. Damm and Andrei G. Fedorov* Multiscale Integrated Thermofluidics Research Lab, GWW School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0405

Transient batch-style reactors (CHAMP) were recently shown to be an attractive alternative to continuousflow reactors for hydrogen production in portable and distributed applications, and idealized kinetic reactor models were used to analyze the performance characteristics. Here, we expand this analysis with the development of a comprehensive batch reactor model which accounts for the effects of mass transport limitations on reactor performance. The relationships between system design parameters and the rate-limiting processes that govern reactor output are identified and mapped out. Additionally, two modes of operation of either constant-volume or constant-pressure reactors are investigated. In constant-volume mode, the residence time is precisely controlled to reach a desired operating state in a trade-off between efficiency and power output without compressing the content of the reaction chamber. In constant-pressure mode, the volume of the reactor is actively reduced by moving a piston along the trajectory that maintains the operating pressure at its maximum allowable value thus enhancing the reactor throughput. Complementary to the theoretical analysis, we report on the development and experimental characterization of two test reactors. The first reactor is a constantvolume batch reactor (no permeable membrane) and provides data on the transient evolution of species concentrations within the reaction chamber. The second reactor incorporates a hydrogen permeable membrane and allows for both constant-volume and variable-volume operation. The experimental data obtained using these reactors are used to validate the predictive value of the reactor model developed in the present study. Introduction

reactor model predictions of fuel conversion and hydrogen yield, experiments were performed on two bench-scale test reactors.

A variable-volume batch-style reactor (CHAMP) has been recently proposed for hydrogen production in portable and distributed applications across a wide range of scales.1 In such a reactor, a discrete amount or batch of fuel mixture is brought into the reaction chamber and held there as long as necessary to achieve the desired performance targets. In the course of mixture residence, reactor conditions are dynamically controlled to ensure that they are favorable for both production and separation of the targeted reaction products. When both the reaction and separation processes have reached a desired level of completion, the remaining mixture is exhausted out of the reaction chamber and a fresh batch of fuel is brought in to repeat the cycle. An idealized kinetic reactor model, neglecting heat and mass transfer limitations, was previously used to calculate the ideal limits of performance and to demonstrate several attractive features of this class of reactors for steam reforming of methanol.1 In that work, the performance of the batch reactor was compared to an analogous continuous flow reactor and it was shown that the batch reactor has the potential for enhanced performance when the number of moles of reaction products is greater than that of reactants. Here, we extend the analysis to investigate more realistic operating scenarios when mass transport limitations are non-negligible. A coupled transportkinetics model is developed, and a parametric study of the reactor operating space is carried out. In order to validate the * To whom correspondence should be addressed. Phone: +1 404 385 1356. Fax: +1 404 894 8496. E-mail: andrei.fedorov@ me.gatech.edu.

Model Formulation A one-dimensional model of the basic embodiment of the CHAMP reactor is developed for simulating the operating cycle. The reactor is composed of three distinct domains (see Figure 1): (1) porous catalyst layer on face of a moving piston, (2) reactor volume between the piston and membrane, and (3) hydrogen selective membrane. Simplifying Assumptions. To simplify the analysis, the following assumptions are made: • the thin porous catalyst layer is assumed to be isothermal (with sufficient heat supplied to maintain the reactions) • intraparticle diffusion and mass transport limitations through the catalyst layer are assumed to be negligible1 (i.e., the effectiveness factor2 is unity) and the reactions occur at the interface between domains 1 and 2 (Figure 1) • the membrane is assumed to be isothermal, at the same temperature as the catalyst, with no external mass transfer limitations on the “permeate” (low pressure) side of the membrane

Figure 1. Major domains of the CHAMP reactor model.

10.1021/ie8015126 CCC: $40.75  2009 American Chemical Society Published on Web 04/28/2009

Ind. Eng. Chem. Res., Vol. 48, No. 12, 2009

• permeation is at quasi-steady state, limited by diffusion through the metallic membrane, and is thus related to the hydrogen partial pressure difference across the membrane according to Sievert’s law3,4 • uniform pressure in the reactor • uniform mass diffusion coefficients for each species based on an “average” mixture composition These simplifying assumptions allow the reactor to be treated as a single domain (2) with the reaction occurring at the boundary between domains 1 and 2 (z ) H) and permeation of hydrogen occurring at the N (z other boundary (z ) 0), which is impermeable to all other A reaction species. ND(z The assumption of an isothermal reactor implies that heat must be supplied to the thin catalyst layer at the same rate it is being consumed by the reactions. It is well-established in the literature5-7 that for continuous-flow (CF) reactors it is difficult to maintain a sufficiently high temperature near the inlet of the channel where the endothermic steam reforming reaction rate is highest (and consumes the most heat), without supplying too much heat further downstream. This is also because of the significantly higher heat transfer coefficient at the entrance of the reactor, where cold reagents are brought into the reactor. This leads to a nonisothermal environment for the catalytic reactions and diminishes the ability to precisely control the composition of the product stream (particularly the formation of CO, which is favored at higher temperatures). On the other hand, in the CHAMP reactor, the heat is applied in a spatially uniform fashion along the catalyst loaded interface 1 (Figure 1) and is readily controlled in the time domain to match the rate of heat consumption due to reaction during each phase of the reaction cycle. The temporal and spatial distribution of five species is considered: (A) methanol, (B) water vapor, (C) carbon dioxide, (D) hydrogen, and (F) carbon monoxide. At the start of a cycle, the reaction chamber is initially filled with methanol and water vapor mixture. These species diffuse to the catalyst surface where they react to form hydrogen, carbon dioxide, and carbon monoxide via the steam reforming reaction, CH3OH + H2O T 3H2 + CO2 ∆H ) 49.2 kJ/mol (1) methanol decomposition reaction, CH3OH T 2H2 + CO ∆H ) 90.4 kJ/mol

(2)

and water gas shift (WGS) reaction, CO + H2O T H2 + CO2 ∆H ) -41.2 kJ/mol

(3)

Hydrogen can permeate in or out of the reactor through the membrane, depending on the direction of the driving force due to the difference between hydrogen partial pressure inside the reactor and that on the permeate side. Governing Equations. The continuity equation for each of the species within the reactor volume (Figure 1) is derived by balancing the time rate of change of moles of species i and the net change in species flow rate through a fixed volume: ∂Ni ∂Ci + )0 ∂t ∂z

(4)

Here, Ci is the molar concentration of the species i, and Ni is the molar flux of species i with respect to a fixed-in-space coordinate frame2 (i.e., the z-coordinate). The molar flux is written as the sum of diffusive and advective components, with the diffusive component defined by Fick’s law, yielding the following governing equations:

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2

∂(CiU) ∂ Ci ∂Ci + ) Di 2 (5) ∂t ∂z ∂z where Di is the mass diffusion coefficient for species i in the multicomponent reaction mixture. The boundary condition for each component at the surface of the membrane (z ) 0) is expressed in terms of molar flux of each species, i, relative to the boundary, which is fixed in space according to the coordinate system defined in Figure 1. ) 0, t) ) NB(z ) 0, t) ) NC(z ) 0, t) ) NF(z ) 0, t) ) 0 Dmemb 1/ 2 (6) (PD (z ) 0) - PD,∞1/ 2) ) 0, t) ) δ Here, Dmemb is the permeability of the hydrogen membrane, PD is the partial pressure of hydrogen at the inside (reactor chamber) surface of the membrane, and PD,∞ is the partial pressure of hydrogen on the permeate side of the membrane. The mass diffusion coefficients are calculated via the semiempirical equation of Gillilland2 for calculating binary diffusion coefficients, DAB. The coefficients were calculated for each combination of pairs of species found in the mixture, i.e., methanol/water vapor, methanol/carbon dioxide, methanol/ hydrogen, water vapor/carbon dioxide, etc. For multicomponent mixtures, the diffusion coefficient of a species through the mixture, Di,m, varies with composition, as well as molar flux of each component. An approximate value for the multicomponent diffusion coefficient can be obtained by assuming that species, A, for example, is diffusing through a stagnant mixture of A, B, C, D, and F, which is calculated from2 DAm )

1 - xA xB /DAB + xC /DAC + xD /DAD + xF /DAF

(7)

This value is calculated for each component diffusing through the mixture using an average mixture composition in the reactor corresponding to 50% methanol conversion. These average values are used for Di in eq 5, and the numerical values calculated at baseline (reference) temperature and pressure are given in Table 1. Also shown are the limiting values of the diffusion coefficient at 0% and 100% conversion. The diffusivities are adjusted in the model for the reactor’s temperature and pressure according to the predictions of kinetic theory, (T/ Tref)3/2 and Pref/P. Additional details on the derivation of the model equations and the solution method can be found in the Supporting Information that is available online. Representative Simulation Results. Several parameters are used to quantify the performance of the reactor. The extent of conversion of fuel to products is given by the parameter χ(t) ) 1 - NA /NA,0

(8)

which increases from 0 at initial time to nearly 1 at full conversion (equilibrium). One possible criterion for completion of a cycle is that conversion has reached x% of its equilibrium value. The total quantity of hydrogen that has permeated through the membrane is the hydrogen yield, given in moles (per unit Table 1. Baseline Diffusion Coefficients

species i (250 °C; 1 atm) methanol water vapor carbon dioxide hydrogen carbon monoxide

multicomponent diffusion coefficient, Di,m (50% MeOH conversion (0-100%); [m2/s]) 5.5 × 10-5 7.2 × 10-5 5.6 × 10-5 12.1 × 10-5 5.3 × 10-5

4.1-6.0 × 10-5 4.1-9.0 × 10-5 3.2-9.5 × 10-5 12.4-11.7 × 10-5 3.7-7.0 × 10-5

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Table 2. Baseline Parameters for Reactor Model model parameters

value [units]

temperature, T initial (or total) pressure, Pinitial initial size of reactor, H0 membrane permeability, Dmemb membrane thickness, δ low side partial pressure of hydrogen, PD∞ effective thickness of catalyst layer, d density of catalyst, Fcat porosity of catalyst, ε specific surface area of catalyst, SA

523 [K] 101.3 [kPa] 0.01 [m] 3.8 × 10-9 [mol/m · s · Pa1/2] 1 × 10-5 [m] 20.26 [kPa] 5 × 10-4 [m] 1300 [kg/m3] 0.5 [-] 102 × 103 [m2/kg]

cross-sectional area normal to the z-direction) Y)

∫

t)τ

t)0

[ ]

Dm 1/ 2 mol (P - PD,∞1/ 2) dt δ D m2

(9)

The cycle-averaged hydrogen yield rate is defined as, Y˙ ) Y/τ, where τ is the residence time of the mixture in the reaction chamber (also referred to as cycle time or contact time). Equally important, the hydrogen yield efficiency provides the ratio of actual hydrogen yield to the “ideal” quantity of hydrogen that could be generated. According to eq 1, the ideal hydrogen yield is equal to three times the initial quantity of methanol, so the hydrogen yield efficiency is simply γ ) Y/3NA,0. Once this value has reached x% of its equilibrium value, the cycle is complete. Note that the equilibrium value of this ratio is less than 100% due to the formation of CO and the nonzero reference hydrogen partial pressure on the permeate side of the membrane. The gross power output of the reactor in terms of hydrogen ˙ H , is estimated by multiplying the rate of production, or W 2 hydrogen production per unit surface area of membrane [mol/ s · m2] by the lower heating value (LHV) of hydrogen (119 950 kJ/kg or 241 820 J/mol8). The power requirement for compressing the reacting mixture (per unit surface area of membrane) is ˙ P ) P (dH/dt), or the product of the total pressure and piston W velocity. Thus, the net power output of the reactor can be found by subtracting the power required for compression from the gross reactor hydrogen output. The baseline set of parameters for the CHAMP design and operation are given in Table 2. The first item of interest in understanding the dynamics of the coupled reaction, transport, permeation, and compression processes is the transient evolution of the component concentration profiles as the fuel is consumed and hydrogen permeates through the membrane. Figure 2 shows concentration profiles of methanol and hydrogen in a constant volume reactor. At very short times, the methanol concentration near the catalyst drops very rapidly with a corresponding rapid increase in hydrogen. The increasing total number of moles near the catalyst pushes the mixture away from the wall, in order to maintain a uniform pressure in the reactor. Evidence of this is seen by the temporary methanol peak near the center of the reactor which is greater in magnitude than the initial concentration (11.6 mol/m3). At the membrane, backpermeation of hydrogen9,10 has the same effect, pushing the mixture toward the center of the reactor. When sufficient hydrogen has been generated by the reactions and has had time to diffuse across the reactor to the surface of the membrane, the elevated hydrogen partial pressure drives permeation forward and out of the reactor. The complete evolution of methanol and hydrogen concentration profiles from t ) 0 to very near equilibrium is shown in Figures 3 and 4, respectively. Methanol conversion greater than 99% is reached after approximately 10 s. Reaching equilibrium for hydrogen requires more time because permeation is delayed

Figure 2. Methanol and hydrogen concentration profiles at very short times (20 µm), power decreases with a slope of 1/δ as expected in a permeation-limited regime. Also, increasing the temperature from 250 to 300 °C has a weak effect on power output because the reactor enters either a diffusion-limited (thin membrane) or permeation-limited (thick membrane) regimesboth processes have relatively weak temperature dependence compared to the reaction rate. The magnitude of the membrane permeability’s temperature dependence can be deduced from the trends on the far right side of the figure, where the reactor is exclusively permeation-limited. The average cycle power and yield efficiency are also affected by the permeate-side hydrogen partial pressure which establishes the set point for the driving force for permeation of hydrogen through the membrane and determines the upper limit of efficiency. In Figure 13, efficiency versus average hydrogen yield (power) is shown for low side partial pressures of 5, 10, 20, 30, and 50% of 1 atm. As the low-side partial pressure decreases, power output increases and the upper limit of efficiency increases. Also shown are lines of constant cycle (residence) time. Because of back permeation very early in the cycle, the average yield and efficiency are both initially negative. This is not a regime for practical operation and is excluded from the figure, which only shows positive values. The best regime for operation is above the dashed line indicated on the figure. Below this line, both the power and efficiency can be increased by holding a longer cycle. Therefore, such a short cycle time is wasteful and unjustified. Eventually, power reaches a maximum (relative to efficiency), and beyond that point, longer cycle times allow higher efficiency by sacrificing the cycle-averaged power output. In the extreme limit of infinite cycle time, the maximum theoretical efficiency would be achieved and the cycle-averaged power would go to zero. It is up to the system designer to determine the mix of efficiency and power that is most appropriate for a particular application. Once a design is chosen, the optimal parameters for operation must be specified. Optimal Reactor Operation. The CHAMP reactor being considered here is operated by filling the reaction chamber with fuel, waiting for the reactions and permeation to proceed to completion, and then pushing the contents of the reaction chamber out through the exhaust valve in preparation for the

Figure 14. Efficiency versus average power output for the baseline CHAMP reactor operated at 225 °C and with various initial displacements, H. Lines of constant residence time, t, scaled by H [s/cm] are indicated.

Figure 15. Efficiency versus average power output for the baseline CHAMP reactor operated at 250 °C and with various initial displacements, H. Lines of constant residence time scaled by H [s/cm] are indicated.

next cycle. Additionally, the reaction chamber volume could be compressed during the waiting period to enhance the yield above that of the fixed volume case. Therefore, the operating parameters are (1) H, the distance that the piston is initially drawn back during the intake stroke, (2) residence time, or time that the mixture remains in the chamber, (3) decision to operate in fixed-volume or variable-volume mode, and (4) if in variablevolume mode, what transient profile of piston motion to employ and the modified residence time that corresponds to the desired efficiency and cycle power. First, consider the case of fixed-volume operation. In Figures 14 and 15, the reactor efficiency and average power output are mapped for operating temperatures of 225 and 250 °C, respectively, and various initial piston displacements, H, of 0.25, 0.5, 1.0, 1.5, and 2.0 cm. Once a reactor size is chosen, the residence time corresponding to a particular combination of power and efficiency can be determined from the map. The residence time, t, is scaled by reactor size, H, and is given in units of seconds per centimeter. Because of mass diffusion in the reaction chamber, the smaller reactor size always gives better


Figure 16. Instantaneous rate of hydrogen yield across multiple cycles for the baseline CHAMP reactor with initial displacement, H, of 0.5 and 1.0 cm. A dead time of 1 s has been added on to the end of each cycle for discharge and refilling.

performance. However, moving along a line of constant t/H implies an increasing frequency of cycles, which brings additional overhead cost and system losses (e.g., friction). The cycle-averaged power output given in the figures is for a single cycle, taking no account for the time required to fill the reactor or discharge it. The quasi-steady output averaged over multiple cycles will be somewhat lower due to this “dead” time between cycles. For example, the transient profiles of instantaneous hydrogen yield rate for several cycles are shown in Figure 16 for initial reactor sizes of 0.5 and 1.0 cm. The cycles are terminated when the efficiency reaches 80%. The dead time between cycles is arbitrarily set at 1 s for the purpose of this example. The 0.5 cm size reactor has a single cycleaveraged hydrogen yield of 0.0246 mol/(m2 s), and the 1.0 cm reactor yield is 14% lower or 0.0211 mol/(m2 s). However, when including the “dead” time in calculations, the quasi-steady output of the reactors over multiple cycles is 0.021 and 0.0196 mol/ (m2 s) for the 0.5 and 1.0 cm reactors, respectively. This is a difference of only 6.7%. The penalty of having to run twice as many cycles to achieve this minimal improvement in power output may or may not be justified. In addition to the fixed-volume mode of operation just described, the CHAMP reactor may also be operated in variablevolume mode. Compressing the reactor with the piston may be desirable if an immediate boost in hydrogen output is required to satisfy a transient load. However, piston motion robs the power output if it is not implemented properly, and compression could increases the total pressure in the reactor excessively, putting a mechanical strain on the delicate membrane, piston seals, tubing connections, and valves. The key to managing the total pressure in the reactor is to match the time scale for piston motion, or velocity, to the rate of hydrogen permeation through the membrane. If the piston motion is faster than hydrogen can permeate, then the pressure rises rapidly. If the piston motion is too slow, then it is ineffectual in driving additional hydrogen through the membrane beyond what would normally occur and instead becomes a parasitic load on the power output of the system. When the rate of hydrogen permeation is precisely matched by the rate of compression, then the pressure remains constant. As already mentioned, the pressure in the reactor initially rises (without active compression) due to the increasing number

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Figure 17. Transient profiles of total pressure and size of reactor, H, for the baseline CHAMP reactor operated in constant-volume (solid lines) and constant-pressure (lines marked with ×) mode.

Figure 18. Efficiency and net power output of the two cases illustrated in Figure 17. In constant-pressure mode (lines marked with ×), both power output and efficiency are higher than in the fixed-volume mode (solid lines).

of moles of products created by the reactions. As the rate of loss of hydrogen due to permeation matches the rate of production via reactions, the pressure reaches a maximum (see Figure 6). The system must be designed to withstand this temporary maximum pressure. Therefore, once the maximum pressure is reached, the piston could be driven forward to maintain the pressure at this elevated value. This, in turn, maximizes the rate of hydrogen permeation under the constraint of a maximum allowable operating pressure. Figure 17 illustrates the pressure profiles and corresponding piston displacements for both constant volume and constant pressure operation. The trajectory of piston motion for the constant-pressure operation is not known a priori, but is adjusted throughout the cycle as needed to keep the pressure at its maximum value. The enhancement in performance is seen in Figure 18 which shows yield efficiency and net power output versus time. Operating the reactor at its maximum allowable pressure enhances both power output and efficiency beyond the fixed-volume case. The net power output was defined previously and takes into account the power required for compression of the reactor volume. The gain, or ratio of marginal reactor power

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reactor in a constant-pressure mode of operation, while allowing the user to choose the balance of power versus efficiency that is appropriate for the application at hand. Experimental Characterization

Figure 19. Efficiency versus power output for the baseline CHAMP reactor operated in constant-pressure mode with various initial sizes, H. The initial pressure for each reactor was 1 atm, and the peak operating pressure was approximately 1.35 atm.

increase to piston power input, is of similar magnitude to that described previously1 (usually greater than 10:1). Countless other trajectories of piston motion are possible, but those that do not exceed the maximum allowable total pressure are bounded on one side by the zero velocity (fixed-volume) case and on the other side by the constant-pressure case just described. If compression were to begin before the pressure peaks, then the magnitude of the pressure peak is required to increase beyond what is allowed. On the other hand, constant pressure operation at a lower total pressure is allowed but does not provide the magnitude of performance enhancement that is achieved by operating at the highest allowable pressure. The constraint of constant, maximum total pressure makes the optimization of the piston trajectory somewhat intuitive. Other constraints, such as desired hydrogen yield efficiency or power output, can lead to entirely different transient profiles of piston motion. The design map in Figure 19 relates the cycle-averaged net power output, and efficiency, to initial reactor size and cycle time for the constant-pressure mode of operation. The piston trajectories and resulting pressures are similar to that shown in Figure 17 and follow the same rule: once the operating pressure reaches its maximum, the piston is driven forward at the precise rate necessary to maintain the pressure at a constant value. Figure 19 provides the information necessary to operate the

Test Setup. Figure 20 shows a schematic diagram of the test reactor and experimental setup. The engineering drawings of the assembled reactor with relevant dimensions, as well as data collected from a nonmembrane reactor are available in the Supporting Information provided online. The piston and cylinder (7.5 cm internal diameter) were machined from aluminum alloy 6061 and supplied with Viton O-rings on the piston to provide a good seal at elevated temperatures. The catalyst was acquired from BASF (F3-01, 1.5 mm diameter × 1.5 mm pellets) and was composed of copper and zinc oxides on a porous aluminum oxide substrate (CuZnAl3O2). A single layer of pellets was held in place on the face of the piston by a copper mesh. The catalyst was reduced in a mixture of 50/50 hydrogen and helium over the catalyst at 180 °C for 1 h per the manufacturer’s directions. The reactor was heated by four Chromalox cartridge heaters (3/8 in. diameter × 1.5 in. length, rated at 120 V and 250 W) embedded inside the piston. The power output of the heaters was controlled by a Tenma variable auto transformer with output of 0-130 V and maximum current of 10 A. The temperature of the catalyst was monitored by thermocouples (Omega Technologies, K-type) embedded 1 mm below the catalyst in the face of the piston and at the other locations shown in the figure. The thermocouples were connected to an Agilent 34970A data acquisition/switch unit which provided continuous temperature readout ((0.05 °C). Prior to running experiments, the entire fixture was brought up to the desired steady-state temperature and the heater controller voltage was set to maintain this temperature while experiments were being run. A syringe pump (World Precision Instruments, SPI100i, with 0.05 mL/h flow rate resolution) was used to pump a precise volume of methanol/water liquid mixture through an evaporator (constructed out of 1/8 in. stainless steel tube wrapped with a flexible Ni-chrome heater) and into the reaction chamber. The temperature of the evaporator was maintained at the same temperature as the catalyst, by setting the voltage on the Tenma heater controller. The membrane was a commercially available [Birmingham Metal Company], 54 µm thick, pure Pd foil forming the cylinder cap or top of the reaction chamber as illustrated in Figure 20. A preheated, metered argon sweep gas (1100 ( 110 sccm, measured by a Cole-Parmer mass flow meter, EW-32464-40) was used to maintain a low partial

Figure 20. Schematic diagram of the experimental setup for testing the prototype membrane reactor.


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Figure 21. Sample plot of mass spectrometer readings of partial pressure of helium, hydrogen, and carbon dioxide during the permeation phase (step 3) and exhaust phase (step 4) of a cycle. During step 3, He and CO2 readings are zero within the resolution of the mass spectrometer, and the only species carried by the sweep gas is hydrogen. When the exhaust valve is opened (4), the contents of the reaction chamber are flushed out by the helium purge.

Figure 22. Hydrogen permeation rate measured by mass spectrometer for two operating temperatures. The lower data sets (1a, 2a, 3a) correspond to an operating temperature of 190 ( 5 °C, while the upper data sets (6-10) are at 250 ( 5 °C.

pressure of hydrogen on the permeate side of the membrane and to carry the hydrogen to a mass spectrometer (Hiden Analytical Quadrapole HPR-20) to measure the hydrogen permeation rate. A discharge valve allowed the contents of the reaction chamber to be sent to the argon sweep gas and carried to the gas analyzer at the conclusion of the cycle. The procedure for performing an experimental run (without piston motion, to establish the baseline performance) was as follows: 1. The entire reactor (reaction chamber + pipes and valves) is purged with helium gas, the piston is in the fully retracted position (H ) 2 ( 0.05 cm), and all valves are closed. The argon sweep gas is flowing on the permeate side of the membrane. 2. Valves A and D (see Figure 20) are opened, and the syringe pump is turned on to deliver 0.1 mL of fuel mixture to displace the helium and fill the reaction chamber. 3. When the filling process is complete, valve D and then valve A are closed; the reactor is left undisturbed for approximately 2 min while the mass spectrometer records the partial pressures of argon, helium, hydrogen, and carbon dioxide (every 0.5 s). Total pressure in the reactor is monitored by a pressure gage (McDaniels Controls, 0-15 psi range with (0.25 psi resolution) and recorded every 5-10 s. 4. The valves B and D are opened, purging the reactor, and sending the mixture to the mass spectrometer.

5. The reactor is prepared for another trial run, and the experiment is repeated several times to ensure reproducibility of results. As seen in Figure 21, the readings of helium and carbon dioxide, relative to the sweep gas, were zero (within the resolution limit of the mass spectrometer) indicating that there were no leaks between the reaction chamber and the argon sweep gas. The flow rate of hydrogen that was produced and permeated across the membrane was calculated using mass spectrometry measurements as described in the Supporting Information available online. Figure 22 shows representative results for the reactor’s hydrogen output (permeated through the membrane) as measured by the mass spectrometer during step 3. The reactor was operated at both 190 and 250 ((5) °C, generating two distinct sets of curves. Most of the spread in the data can be attributed to limitations in the ability to precisely control the initial conditions from one cycle to the next. Pressure measurements indicated that the initial pressure was between (1.5-3.0) ( 0.25 psi above atmospheric pressure. This implies that some of the helium purge gas may have remained in the reaction chamber during the cycle. Under the operating conditions of these experiments, the hydrogen yield is limited both by the rate of permeation through the membrane and mass transport in the bulk gas phase of the reactor. The driving force for permeation of hydrogen through

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Figure 23. Transient profiles of hydrogen permeation rate ((11%) with and without volume compression. The experiments 6, 9, and 10 are operated under baseline conditions (constant volume) while runs 11, 14, and 15 show enhanced hydrogen yield as a result of midcycle compression of the reaction chamber.

the membrane is the partial pressure of hydrogen near the surface of the membrane (for a given partial pressure at the permeate side), and as hydrogen becomes depleted in the reactor, the permeation rate falls. By compressing the volume of the reactor, the hydrogen permeation rate can be maintained above the baseline (constant volume) value. To demonstrate this, the experiments were repeated with the piston moving forward during the cycle in order to shorten the diffusion length and to maintain an elevated partial pressure of hydrogen. The procedure for experiments with piston motion was similar to that listed above, with the following modification to step 3: When the filling process is complete, ValVe D and then ValVe A are closed; the reactor is left undisturbed for a fixed amount of time (e.g., 15, 20, 25 s); the piston driVing screw is driVen forward 1.25 turns in 10 s which corresponds to a linear speed of 0.5 mm/s; the reactor is left undisturbed again; meanwhile, the mass spectrometer records the partial pressures of argon, helium, hydrogen, and carbon dioxide. Pressure in the reactor is monitored and recorded eVery 5-10 s. The experimental results with piston motion (linear volume compression) are plotted in Figure 23 superimposed on data from the baseline cases of fixed volume reactor operating at the same initial pressure. A clear enhancement of the hydrogen production (permeation) rate is observed when the volume is compressed midcycle. This is primarily due to the increased partial pressure of hydrogen in the reactor which is the driving force for permeation. Model Validation. The experimental results reported in the previous section demonstrate the feasibility of building and operating the variable volume, batch-membrane reactor. Additionally, the time evolution of hydrogen yield for the baseline (fixed volume) case and the hydrogen yield enhancement enabled by compression of the volume are in agreement with theoretical predictionssthus validating the present understanding of the key operating principles of the CHAMP reactor. Of particular significance is the ability of the just described numerical reactor model to predict the performance of the real reactor both qualitatively and quantitatively. In the model, the hydrogen flux permeating the membrane is assumed to follow the relationship, J ) (D0/δ)(PH21/2 - P∞1/2), as described

previously. The membrane permeability, D0, was measured for the 54 µm thick palladium foil to be D0 ) 4.1 × 10-6 exp[-1387.9/T][mol · m/(m2 s kPa1/2)] using a reagent grade hydrogen-helium mixture with no contaminants.13 However, there is considerable evidence reported in the literature that the presence of the species found in the reacting mixture (CH3OH, H2O, CO2, and CO) can have a deleterious effect on the membrane permeability, either through competitive adsorption or blocking of active sites on the surface. Carbon monoxide in the mixture has been singled out as being especially harmful, even at concentrations less than 1% by volume; although its effect on membrane permeability is reversible (i.e., membrane is not “poisoned”). For example, Amandusson14 tested a 25 µm thick palladium membrane and reported a 10% decrease in the ideal (pure gas) permeation rate when the retentate mixture contained equal parts hydrogen and carbon monoxide. This was measured at a membrane temperature of 250 °C, but much more severe COinduced drops in permeability were reported at lower temperatures at which surface reactions play a significant role in determining the total hydrogen flux through the membrane. On the other hand, Cheng15 reported that permeation through a palladium membrane decreased to 1/5 of its initial (pure gas) rate when exposed to a Towngas mixture (CH4, CO2, H2, and CO), although this effect was partially ameliorated in palladiumsilver (Pd-Ag) membranes. In a more comprehensive study, Chabot16 tested a 250 µm thick Pd-Ag membrane to measure the hydrogen flux for gas mixtures with small amounts of CO. Even with very small concentrations (e.g., 0.2 vol %) of CO in the hydrogen stream, the inhibiting effect can be significant. As seen in Figure 24, the inhibiting effect of CO depends strongly on temperature, but once the volume fraction of CO exceeds 5-10%, the membrane surface becomes “saturated” and higher levels of CO have little effect. Also at play is the transition between the rate limiting steps for permeation through the membrane. At higher temperatures (and with thicker membranes), the permeation is limited by diffusion through the solid Pd-alloy bulk and surface effects have negligible influence on the hydrogen flux. The


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Figure 25. Dependence of membrane permeability on CO concentration (k0 ) 0.58, A ) 0.0016).

Figure 24. Inhibiting effect of various CO concentrations on the hydrogen permeation through a Pd-Ag membrane.16

membrane of the work of Chabot16 is nearly five times thicker (250 µm) than in the present study (54 µm); therefore, it is expected that surface effects (and CO in the mixture) in our experiments will be even more noticeable and should be taken into account. Most recently, Peters3 tested an ultrathin Pd-Ag membrane (2.2 µm) at 400 °C and reported approximately a 50% decrease in permeation due to the presence of 5% CO by volume. The flux (relative to its ideal value) appears to fall with an exponential dependence on the molar fraction of CO in the feed (see Figure 6 in the referenced work), implying that the permeability roughly follows the relationship, D ) 1 - k0 exp[-A/xCO] D0

(10)

The pre-exponential, k0 and the constant, A, can be approximated from the data reported3 and can be adjusted to provide a better fit to the experimental data presented here. This equation is plotted in Figure 25, showing the relationship between relative flux and concentration of CO. As the mole fraction of CO goes to zero, the relative permeability approaches 1. As the mole fraction increases beyond 5%, the relative permeability levels off and increasing the concentration of CO has little effect. The reactor model was modified so that the permeability of the membrane depends on CO concentration at the surface of the membrane according to eq 10. Figure 26 shows the model predictions of hydrogen yield compared to a representative experimental run. Also shown is the CO concentration at the surface of the membrane, which affects the membrane permeability in the manner just described. The model tends to overpredict the hydrogen permeation rate initially and then predicts a more rapid drop of the rate as the hydrogen becomes depleted. This discrepancy can be explained not only by multidimensional effects (the test reactor is not truly 1D) but also by the presence of helium used as a purge gas in the experiments, which dilutes the fuel mixture and diminishes the expected pressure rise in the reactor. (A 2:1 ratio of moles of products to reactants is expected, but the presence of a diluent

lowers this ratio and hence the expected pressure rise.) Ultimately, the diluted mixture results in a smaller driving force for permeation, hence, a reduced hydrogen flow rate that has been measured, as compared to predicted values. The initial pressure in the reactor was slightly above atmospheric (1.2 atm or 17.5 psi) as can be seen in Figure 27. It is reasonable to assume that this excess pressure corresponds to undisplaced helium from the filling process. That is, the fuel mixture is diluted with approximately 17% helium (0.2 atm/ 1.2 atm). The numerical reactor model was solved for this dilute mixture case (including helium as an additional, but nonreacting species), which resulted in improved quantitative prediction of both hydrogen yield and total pressure inside the reactor as seen in Figures 26 and 27. The model is also able to predict qualitatively and quantitatively the hydrogen output and pressure in the reactor when the volume is compressed by the piston. In Figure 28, the experimental data on hydrogen permeation rate from experiments 9 (constant volume) and 11 (with compression) are compared to the corresponding model predictions. The model assumes a dilute (with residual helium) fuel mixture as previously described. Similarly, in Figure 29, the pressure data from experiments 10 (constant volume) and 15 (with compression) are compared to the corresponding model predictions, with good agreement. Concluding Remarks The coupled mass transport-reaction kinetics-membrane separation model has been developed and used to investigate the optimal design and operation of variable-volume transient batch (CHAMP) reactors. The transitions between reaction limited, permeation limited, and diffusion limited regimes have been mapped out and provide insight into optimization of the design parameters including temperature, reactor size, membrane thickness, and permeate-side hydrogen partial pressure. Once a specific design is chosen, the optimal operating parameters could be selected using the performance map developed, including initial displacement of the piston, residence time, and transient profile of piston motion (if any). In fixed-volume mode of operation, the residence time is precisely controlled to provide the desired trade-off between efficiency and power output. Recognizing that the reactor can operate at an elevated constant pressuresmaintained by a pressure-following piston trajectorysopens up otherwise inac-

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Figure 26. Comparison of experimentally measured hydrogen flux (run 9 in Figure 23, flux measurement uncertainties (11%) and model predictions of hydrogen yield rate. The baseline initial condition assumes a pure fuel mixture in the reactor, while the dilute model assumes that the fuel mixture was initially diluted by helium (17%) that remains in the reaction chamber. Also, shown is the model prediction of molar concentration of carbon monoxide at the surface of the membrane.

Figure 27. Comparison of experimental data and model predictions of total pressure in the reactor. The uncertainty in pressure and time measurements are (0.25 psi and (0.5 s, respectively. The baseline and dilute models are the same as those in Figure 26.

Figure 28. Experimental data and model predictions of hydrogen output for the baseline case (constant volume) and the case with midcycle compression of the reactor volume.

cessible regions of the efficiency-power parameter space. This ability to dynamically control the reactor volume, midcycle, to achieve the desired blend of efficiency and power is unique to the CHAMP class of reactors. To complement the theoretical study, experimental characterization of a laboratory scale reactor is also reported. The experimental results obtained with prototype reactors support

Figure 29. Transient pressure profiles in the reactor with and without volume compression. The initial pressure for these cases was 1.1 atm, and the corresponding dilution of the fuel was 10% helium.

the feasibility of operating a variable-volume, batch, membrane reactor with expected performance gains. More importantly, the results validate the ability of the theoretical model to predict the hydrogen output with reasonable accuracy. The experimental results obtained provide an unambiguous validation of the key operating principles of CHAMP reactors for hydrogen production including (1) verification that the expected dominant reaction is steam reforming of methanol, (2) usefulness of the coupled reaction kinetics, membrane permeation, mass transfer, and volume compression models for predicting the rate of hydrogen yield, and (3) the ability to operate the batch reactor in both fixed-volume and variable-volume modes with an increased rate of hydrogen production. Future efforts include development of an improved test reactor with comprehensive, automatically controlled measurement infrastructure to enable experimental characterization of the reactor performance for a broader range of operating conditions. In particular, the improved test reactor should have a thinner membrane (

Batch Reactors for Hydrogen Production: Theoretical Analysis and

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